# Homework Help: Is the sequence {n/(n^2+1)} convergent, and if so, what is it's limit? I think Yes

1. Apr 26, 2012

### mmilton

1. The problem statement, all variables and given/known data

Is the sequence {n/(n^2+1)} convergent, and if so, what is it's limit?

2. Relevant equations

3. The attempt at a solution

I believe it does converge because the higher power is in the denominator, so thus, it's limit is 0.

Any help or hints on if I'm headed in the right direction would be very much appreciated!

2. Apr 26, 2012

### stony

Re: Is the sequence {n/(n^2+1)} convergent, and if so, what is it's limit? I think Ye

You are right, using the rules you've learned about infinity limits will get us ((1/n)/(1+(1/n^2))) and the limit of that as n approaches infinity is 0.

3. Apr 27, 2012

### SammyS

Staff Emeritus
Re: Is the sequence {n/(n^2+1)} convergent, and if so, what is it's limit? I think Ye

Multiply the numerator & denominator by 1/n .

4. Apr 27, 2012

### Whovian

Re: Is the sequence {n/(n^2+1)} convergent, and if so, what is it's limit? I think Ye

If you're talking about the SEQUENCE, then it converges. Use a useful little rule known as L'Hôpital.

If you're talking about the SERIES, use the Ratio or Integral tests. It diverges.